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        <td class="header">&nbsp; Polarimetric Classification<br>
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<h3>Polarimetric Classification Operator</h3>&nbsp;&nbsp;&nbsp;This operator performs the following polarimetric
classification for a full polarimetric SAR product:<br>
<ul>
    <li>Unsupervised Cloude-Pottier Classification<br>
    </li>
    <li>Unsupervised Whishart Classification</li>
</ul>
<h4>Cloude-Pottier Classification<br>
</h4>&nbsp;&nbsp; The Cloude-Pottier classification is an unsupervised
classification scheme which is based on the use of the Entropy (H) /
Alpha (<span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;;" lang="EN-US">&#945;</span>)
plane. Entropy by definition is a natural measure of the inherent
reversibility of the scattering data while alpha can be used to
identify the underlying average scattering mechanisms. The H / Alpha
plane is divided into nine zones corresponding to nine classes of
different scattering mechanisms. For each pixel in the source product,
its entropy and alpha angle are computed. Based on the position of the
computed entropy and alpha in the H / Alpha plane, the pixel is
classified into one of the nine zones, a zone index is assigned to the
pixel. For detail calculations of entropy and alpha, readers are
referred to on-line help for Polarimetric Decomposition operator.
Figure 1 shows the locations and boundaries of the nine zones in H /
Alpha plane:<br>
&nbsp;&nbsp; <br>
<img style="width: 710px; height: 533px;" alt="" src="images/polarimetricClassificationHAlphaPlane.jpg"><br>

<div style="margin-left: 280px;">Figure 1. H / Alpha plane<br>
</div>
<h4>H Alpha Wishart Classification</h4>&nbsp;&nbsp; Similar to the
Cloude-Pottier classification, the unsupervised H Alpha Wishart classification
also separates data into nine clusters using the zones defined in
the&nbsp; H / Alpha plane above. Different from the Cloude-Pottier
classification, the H Alpha Wishart classification will continue to compute the
centres of the nine clusters, then reclassify the pixels based on their
Wishart distances to the cluster centres. This procedure will repeat
several times until the user defined total number of
iterations is reached. To achieve accurate classification result, speckle filtering must be applied before the
classification.<br>
<br>
&nbsp;&nbsp; The cluster centre<span style="font-style: italic;"> V<sub>m</sub></span> for the <span style="font-style: italic;">m</span>th cluster is the average of the coherency matrices<sub></sub> of all pixels
in the cluster. Mathematically it is given by <br>

<div style="margin-left: 120px;"><img style="width: 116px; height: 49px;" alt="" src="images/polarimetricClassification_eq1.jpg"><br>
</div>
<br>
&nbsp;&nbsp; The Wishart distance measure from coherency matrix <span style="font-style: italic;">T</span> to cluster
centre <span style="font-style: italic;">V<sub>m</sub></span> is defined<span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; font-style: italic;"></span><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; font-style: italic;"></span><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; font-style: italic;"></span><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; font-style: italic;"></span><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;;"><span style="font-style: italic;"></span></span><span style="font-size: 12pt; font-family: &quot;Times New Roman&quot;; font-style: italic;"></span><span style="font-style: italic;"></span><span style="font-style: italic;"></span><span style="font-style: italic;"></span> as the following:<br>
<br>

<div style="margin-left: 120px;"><img style="width: 204px; height: 35px;" alt="" src="images/polarimetricClassification_eq2.jpg"><br>
</div>
&nbsp;&nbsp; <br>
&nbsp;&nbsp; where ln() is the natural logarithm function, |.| and
Tr(.) indicate the determinant and the trace of the matrix respectively.<br>
<h4>Freeman-Durden Wishart Classification</h4>
&nbsp; The Freeman-Durden classification is also a Wishart distance
based classification. It basically implements the unsupervised PolSAR
classification algorithm proposed by Lee et al. in [2]. In the
algorithm, the pixels are first divided into three categories of
surface, volume and double bounce scattering by applying the
Freeman-Durden decomposition. Then 30 clusters are created in each
category with approximately equal number of pixels based on the
backscattering power of surface, volume and double bounce. Finally the
clusters in each category are merged to a pre-selected number of
classes based on Wishart distance between clusters.<br><h4>General Wishart Classification</h4>
&nbsp;&nbsp; The General Wishart classification method
generalizes&nbsp;the Freeman-Durden Wishart classification method
above.&nbsp; In the General Wishart classification, the initial
decomposition method is generalized from Freeman-Durden method to other
decomposition method, such as Sinclair decomposition, Yamaguchi
decomposition etc. The rest of the algorithm is the same as the
Freeman-Durden classification algorithm.<br>

<h4>Input and Output</h4>

<ul>
    <li>The
        input to this operator can be covariance
        matrix or coherency
        matrix generated by Polarimetric Matrix Generation operator.
    </li>
    <li>The output of this operator is a band with pixel values being the cluster indices.</li>
</ul>
<ol>
</ol>
<h4>Parameters Used</h4>&nbsp;&nbsp; For Cloude-Pottier classification, the following processing parameter are needed
(see Figure 2):<br>
<ul>
    <li>Classification: the classification method</li>
    <li>Window Size: dimension of sliding window for computing mean covariance or coherency matrix</li>
</ul>
<br>
<img style="width: 438px; height: 443px;" alt="" src="images/polarimetricClassification_cloude_pottier.jpg"><br>

<div style="text-align: left;">&nbsp;&nbsp;&nbsp;
    &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;
    &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;
    &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;
    &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;
    &nbsp;&nbsp;&nbsp; <br>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;
    &nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp; &nbsp;Figure 2. Dialog box for&nbsp;Cloude-Pottier classification<br>
</div>
<br><br>
For H Alpha Wishart classification, the following parameters are used (see Figure 3):<br>
<ul>
    <li>Classification: the classification method</li>
    <li>Window Size: dimension of sliding window for computing mean covariance or coherency matrix</li>
    <li>Maximum Number of Iterations: the maximum number of iterations<br>
    </li>
</ul>
<img style="width: 437px; height: 443px;" alt="" src="images/polarimetricClassification_unsupervised_wishart.jpg"><br><br>&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;
&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp; Figure 3. Dialog box for H Alpha Wishart classification<br>
<br>
For the Freeman-Durden Wishart classification, the following parameters are used (see Figure 4):<br>
<ul>
    <li>Classification: the classification method</li>
    <li>Window Size: dimension of sliding window for computing mean covariance or coherency matrix</li>
    <li>Initial Number of Classes: the initial number of clusters</li>
    <li>Final Number of Classes: the final number of classes after classification</li>
    <li>Threshold for Mixed Category: the threshold used in classifying
        pixels to the mixed category. The Freeman-Durden decomposition computes
        for each pixel the contribution of three scattering mechanisms: volume,
        surface and double-bounce. Based on the dominant value of the three
        categories, the pixel is classified to one of the categories. But for
        some pixels, there is no obvious dominant value, in this case the pixel
        is classified to the mixed category. Say the pixel has values Pv, Ps
        and Pd for the three categories, if max(Pv, Ps, Pd) / (Pv + Ps + Pd)
        &lt;= this threshold, it is classified to the mixed category.<br>
    </li>

</ul>

<p><img style="width: 437px; height: 443px;" alt="" src="images/polarimetricClassification_unsupervised_freeman_durden_wishart.jpg"><br>
</p>

<p>Figure 4. Dialog box for the Freeman-Durden Wishart classification</p><p></p>

<p>
For the General Wishart classification, the following parameters are used (see Figure 4):<br>
</p><ul><li>Classification: the classification method</li><li>Window Size: dimension of sliding window for computing mean covariance or coherency matrixp</li><li>Initial Number of Classes: the initial number of clusters</li><li>Final Number of Classes: the final number of classes after classification</li><li>Threshold for Mixed Category: the threshold used in classifying
        pixels to the mixed category</li><li>Decomposition: The initial decomposition method. The following decomposition methods are currently supported: Sinclair, Pauli, Freeman-Durden, Generalized Freeman-Durden, Yamaguchi, van Zyl, Cloude and Touzi</li></ul><p>

<img style="width: 435px; height: 444px;" alt="" src="images/polarimetricClassification_unsupervised_general_wishart.jpg"></p><p>Figure 5. Dialog box for the General Wishart classification</p><p></p>

<p> Reference:&nbsp;</p>

<p>[1] J.S. Lee and E. Pottier, Polarimetric Radar Imaging: From Basics to Applications, CRC Press, 2009</p>

<p>[2] J.S. Lee, M.R. Grunes, and E. Pottier, "Unsupervised terrain
    classification preserving polarimetric scattering characteristics",
    IEEE Transaction on Geoscience and Remote Sensing, Vol. 42, No. 4,
    April 2004.<br>
    <br>
</p>


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